TSTP Solution File: BOO011-4 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : BOO011-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 14 23:47:59 EDT 2022
% Result : Unsatisfiable 0.72s 1.01s
% Output : Refutation 0.72s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : BOO011-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.06/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Wed Jun 1 20:02:01 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.72/1.01 ============================== Prover9 ===============================
% 0.72/1.01 Prover9 (32) version 2009-11A, November 2009.
% 0.72/1.01 Process 16805 was started by sandbox2 on n029.cluster.edu,
% 0.72/1.01 Wed Jun 1 20:02:01 2022
% 0.72/1.01 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_16652_n029.cluster.edu".
% 0.72/1.01 ============================== end of head ===========================
% 0.72/1.01
% 0.72/1.01 ============================== INPUT =================================
% 0.72/1.01
% 0.72/1.01 % Reading from file /tmp/Prover9_16652_n029.cluster.edu
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% 0.72/1.01 set(prolog_style_variables).
% 0.72/1.01 set(auto2).
% 0.72/1.01 % set(auto2) -> set(auto).
% 0.72/1.01 % set(auto) -> set(auto_inference).
% 0.72/1.01 % set(auto) -> set(auto_setup).
% 0.72/1.01 % set(auto_setup) -> set(predicate_elim).
% 0.72/1.01 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.72/1.01 % set(auto) -> set(auto_limits).
% 0.72/1.01 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.72/1.01 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.72/1.01 % set(auto) -> set(auto_denials).
% 0.72/1.01 % set(auto) -> set(auto_process).
% 0.72/1.01 % set(auto2) -> assign(new_constants, 1).
% 0.72/1.01 % set(auto2) -> assign(fold_denial_max, 3).
% 0.72/1.01 % set(auto2) -> assign(max_weight, "200.000").
% 0.72/1.01 % set(auto2) -> assign(max_hours, 1).
% 0.72/1.01 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.72/1.01 % set(auto2) -> assign(max_seconds, 0).
% 0.72/1.01 % set(auto2) -> assign(max_minutes, 5).
% 0.72/1.01 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.72/1.01 % set(auto2) -> set(sort_initial_sos).
% 0.72/1.01 % set(auto2) -> assign(sos_limit, -1).
% 0.72/1.01 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.72/1.01 % set(auto2) -> assign(max_megs, 400).
% 0.72/1.01 % set(auto2) -> assign(stats, some).
% 0.72/1.01 % set(auto2) -> clear(echo_input).
% 0.72/1.01 % set(auto2) -> set(quiet).
% 0.72/1.01 % set(auto2) -> clear(print_initial_clauses).
% 0.72/1.01 % set(auto2) -> clear(print_given).
% 0.72/1.01 assign(lrs_ticks,-1).
% 0.72/1.01 assign(sos_limit,10000).
% 0.72/1.01 assign(order,kbo).
% 0.72/1.01 set(lex_order_vars).
% 0.72/1.01 clear(print_given).
% 0.72/1.01
% 0.72/1.01 % formulas(sos). % not echoed (9 formulas)
% 0.72/1.01
% 0.72/1.01 ============================== end of input ==========================
% 0.72/1.01
% 0.72/1.01 % From the command line: assign(max_seconds, 300).
% 0.72/1.01
% 0.72/1.01 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.72/1.01
% 0.72/1.01 % Formulas that are not ordinary clauses:
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% 0.72/1.01 ============================== end of process non-clausal formulas ===
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% 0.72/1.01 ============================== PROCESS INITIAL CLAUSES ===============
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% 0.72/1.01 ============================== PREDICATE ELIMINATION =================
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% 0.72/1.01 ============================== end predicate elimination =============
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% 0.72/1.01 Auto_denials:
% 0.72/1.01 % copying label prove_inverse_of_1_is_0 to answer in negative clause
% 0.72/1.01
% 0.72/1.01 Term ordering decisions:
% 0.72/1.01
% 0.72/1.01 % Assigning unary symbol inverse kb_weight 0 and highest precedence (6).
% 0.72/1.01 Function symbol KB weights: additive_identity=1. multiplicative_identity=1. add=1. multiply=1. inverse=0.
% 0.72/1.01
% 0.72/1.01 ============================== end of process initial clauses ========
% 0.72/1.01
% 0.72/1.01 ============================== CLAUSES FOR SEARCH ====================
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% 0.72/1.01 ============================== end of clauses for search =============
% 0.72/1.01
% 0.72/1.01 ============================== SEARCH ================================
% 0.72/1.01
% 0.72/1.01 % Starting search at 0.01 seconds.
% 0.72/1.01
% 0.72/1.01 ============================== PROOF =================================
% 0.72/1.01 % SZS status Unsatisfiable
% 0.72/1.01 % SZS output start Refutation
% 0.72/1.01
% 0.72/1.01 % Proof 1 at 0.04 (+ 0.01) seconds: prove_inverse_of_1_is_0.
% 0.72/1.01 % Length of proof is 24.
% 0.72/1.01 % Level of proof is 7.
% 0.72/1.01 % Maximum clause weight is 13.000.
% 0.72/1.01 % Given clauses 38.
% 0.72/1.01
% 0.72/1.01 1 add(A,additive_identity) = A # label(additive_id1) # label(axiom). [assumption].
% 0.72/1.01 2 multiply(A,multiplicative_identity) = A # label(multiplicative_id1) # label(axiom). [assumption].
% 0.72/1.01 3 add(A,inverse(A)) = multiplicative_identity # label(additive_inverse1) # label(axiom). [assumption].
% 0.72/1.01 4 multiply(A,inverse(A)) = additive_identity # label(multiplicative_inverse1) # label(axiom). [assumption].
% 0.72/1.01 5 add(A,B) = add(B,A) # label(commutativity_of_add) # label(axiom). [assumption].
% 0.72/1.01 6 multiply(A,B) = multiply(B,A) # label(commutativity_of_multiply) # label(axiom). [assumption].
% 0.72/1.01 7 add(A,multiply(B,C)) = multiply(add(A,B),add(A,C)) # label(distributivity1) # label(axiom). [assumption].
% 0.72/1.01 8 multiply(add(A,B),add(A,C)) = add(A,multiply(B,C)). [copy(7),flip(a)].
% 0.72/1.01 9 multiply(A,add(B,C)) = add(multiply(A,B),multiply(A,C)) # label(distributivity2) # label(axiom). [assumption].
% 0.72/1.01 10 add(multiply(A,B),multiply(A,C)) = multiply(A,add(B,C)). [copy(9),flip(a)].
% 0.72/1.01 11 inverse(additive_identity) != multiplicative_identity # label(prove_inverse_of_1_is_0) # label(negated_conjecture) # answer(prove_inverse_of_1_is_0). [assumption].
% 0.72/1.01 13 multiply(multiplicative_identity,add(A,B)) = add(A,multiply(B,inverse(A))). [para(3(a,1),8(a,1,1)),rewrite([6(5)])].
% 0.72/1.01 14 multiply(add(A,B),add(B,C)) = add(B,multiply(A,C)). [para(5(a,1),8(a,1,1))].
% 0.72/1.01 16 multiply(A,add(B,inverse(A))) = add(additive_identity,multiply(A,B)). [para(4(a,1),10(a,1,1)),rewrite([5(5)]),flip(a)].
% 0.72/1.01 54 multiply(multiplicative_identity,add(A,B)) = add(B,multiply(A,inverse(B))). [para(13(a,2),5(a,2)),rewrite([5(3),5(5)]),flip(a)].
% 0.72/1.01 59 add(A,multiply(B,inverse(A))) = add(A,B). [para(13(a,1),10(a,2)),rewrite([6(2),2(2),6(2),2(2)]),flip(a)].
% 0.72/1.01 70 multiply(multiplicative_identity,add(A,B)) = add(A,B). [back_rewrite(54),rewrite([59(6),5(4)])].
% 0.72/1.01 88 add(additive_identity,multiply(A,B)) = multiply(A,B). [para(1(a,1),14(a,1,1)),rewrite([5(2),1(2)]),flip(a)].
% 0.72/1.01 96 multiply(A,add(B,inverse(A))) = multiply(A,B). [back_rewrite(16),rewrite([88(6)])].
% 0.72/1.01 137 multiply(A,inverse(additive_identity)) = A. [para(59(a,1),88(a,1)),rewrite([5(2),1(2)]),flip(a)].
% 0.72/1.01 183 add(A,inverse(multiplicative_identity)) = A. [para(96(a,1),70(a,1)),rewrite([6(2),2(2)]),flip(a)].
% 0.72/1.01 187 multiply(A,add(inverse(A),inverse(additive_identity))) = A. [para(137(a,1),96(a,2)),rewrite([5(4)])].
% 0.72/1.01 193 inverse(additive_identity) = multiplicative_identity. [para(187(a,1),70(a,1)),rewrite([5(6),183(6)]),flip(a)].
% 0.72/1.01 194 $F # answer(prove_inverse_of_1_is_0). [resolve(193,a,11,a)].
% 0.72/1.01
% 0.72/1.01 % SZS output end Refutation
% 0.72/1.01 ============================== end of proof ==========================
% 0.72/1.01
% 0.72/1.01 ============================== STATISTICS ============================
% 0.72/1.01
% 0.72/1.01 Given=38. Generated=847. Kept=191. proofs=1.
% 0.72/1.01 Usable=32. Sos=104. Demods=114. Limbo=1, Disabled=62. Hints=0.
% 0.72/1.01 Megabytes=0.20.
% 0.72/1.01 User_CPU=0.04, System_CPU=0.01, Wall_clock=0.
% 0.72/1.01
% 0.72/1.01 ============================== end of statistics =====================
% 0.72/1.01
% 0.72/1.01 ============================== end of search =========================
% 0.72/1.01
% 0.72/1.01 THEOREM PROVED
% 0.72/1.01 % SZS status Unsatisfiable
% 0.72/1.01
% 0.72/1.01 Exiting with 1 proof.
% 0.72/1.01
% 0.72/1.01 Process 16805 exit (max_proofs) Wed Jun 1 20:02:01 2022
% 0.72/1.01 Prover9 interrupted
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